Solve for $x$ and $y$ using elimination. $\begin{align*}-2x-8y &= 1 \\ 2x+4y &= -2\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-4y = -1$ Divide both sides by $-4$ and reduce as necessary. $y = \dfrac{1}{4}$ Substitute $\dfrac{1}{4}$ for $y$ in the top equation. $-2x-8( \dfrac{1}{4}) = 1$ $-2x-2 = 1$ $-2x = 3$ $x = -\dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{3}{2}, \enspace y = \dfrac{1}{4}$.